What we expect of morality

When I try to think of the barest, most minimal requirements I have for something to be recognizable to me as morality, I end up with something like this: "Morality is a way of evaluating at least some possibilities of things we can do, or who and how we can be." Now, this is a pretty minimal specification; any evaluative scheme at all could fit this bill. But many people make much more substantial assumptions about what morality must be like. And they often do so without defending those assumptions (which is not to say that they should be defending them; it just means that I haven't seen much discussion of these ideas).

Here are some examples:

• Morality should be a simply-describable function. The inputs to the function will be actions (or perhaps biographies), and the outputs will be evaluations. The function itself will be describable by a fairly short list of rules.
• Morality involves publicly-expressed reasons. If we judge a certain thing morally good, then we must be able to give an intelligible account of why that thing is good, and what it would take to change that good thing into a bad thing. If we have moral judgments that we can't back up with reasons, then those are not real moral judgments at all, but rather psychological biases or distortions. (I take this to be more or less what Peter Unger thinks, after reading parts of Living High and Letting Die.)
• Morality should judge my individual confrontation with possibilities in the world. If it is right for me to act a certain way, a change in the behavior of those around me can't make it wrong for me to act that way. (This seems absurd to me, but I hear it suggested by classmates, and see it expressed in a more limited domain as the "Compliance Condition" in Liam Murphy's "The Demands of Beneficence".)
• Morality applies only when our actions affect other people.

Probably there are more -- I'll keep collecting them here as I find them. The next questions are which of these make sense to include in our conception of morality, and how we would go about deciding that.